Start at https://www.detectorprospector.com/magazine/steves-guides/metal-detecting-and-prospecting-library/
Especially these two:
How Metal Detectors Work by Mark Rowan & William Lahr - Originally published by White's Electronics as a booklet P/N 621-0395. Basic but rather technical information on how induction balance and pulse induction metal detectors work.
Metal Detector Basics and Theory by Bruce Candy - Bruce is a co-founder of Minelab and the man behind their most advanced designs. This information delves into much greater detail than the above link and has many more illustrations and diagrams.
Before Carl Moreland was Engineering Manager at White's Electronics (and now First Texas), he created a website that has more technical information on metal detectors than any I know of. The Geotech website has lots of interesting stuff and in particular it has a lot of "build your own" metal detector projects for the electronically minded. I have never done this myself but if you were ever curious about what makes detectors tick a lot can be learned here.
Projects http://www.geotech1.com/cgi-bin/pages/common/index.pl?page=metdet&file=projects.dat
Info http://www.geotech1.com/cgi-bin/pages/common/index.pl?page=metdet&file=info.dat
George Overton & Carl Moreland, co-admins for the Geotech web site, also wrote the new book, Inside the Metal Detector. This is not another "how to use a metal detector" but rather a look inside to the operating principles and electronics that make a detector work.
Inside the Metal Detector explains theory and offers numerous experiments and projects that demonstrate the theory. You can build an off-resonance pinpointer, a GEB-discriminator, and a microprocessor-controlled PI detector. Even if you're not inclined to build a detector, the concepts learned from ITMD will help you better understand how your own detector works and what all those controls are really doing. The book can be purchased in paperback or Kindle versions on Amazon